I did not expect much from the movie adaptation of 21 Jump Street that opened last weekend, and not because I loved the original so much that I was worried for its legacy. I watched the late-’80s Johnny Depp original occasionally, enough to recall its style and its outline, but if anything, I was worried that the movie version would be so fixated on the details of the original that it would lose me.

Instead, the movie–deservedly successful at the box office–was a textbook example of the best way to adapt a TV show for the big screen: by using the source material as a jumping-off point to make an entirely new, and at least somewhat original, movie that works not the way TV shows do but the way movies do.

We’ve seen a lot of TV shows remade as movies in the past couple decades from the movie as reboot of the TV original (Charlie’s Angels) to the movie as extension of the TV show (Sex and the City, The Simpsons) to the movie as resolution (Serenity) to the movie as loving parody (Starsky and Hutch). Jump Street arguably fits into the last category, but only barely. It’s a comedy where the Fox cop show was a drama, but it doesn’t continue the characters (except for a brilliant curtain call that I won’t spoil here) so much as it borrows the premise.

And rather than rationalize the silliness of that premise—cops who clearly look too old to be teens going undercover at a high school—the Jump Street movie leans into it. Schmidt (Jonah Hill) and Jenko (Channing Tatum) are hapless new cops who are recruited to bust a high school drug ring, getting the assignment in a meta moment from Nick Offerman (in a perfectly cast if too-small Grouchy Guy Behind a Desk role), who tells them the department is reviving a program from the 1980s because “nobody has any new ideas anymore.”

What really makes the Jump Street movie work is an idea that’s all its own: it plays with the idea that Schmidt and Jenko (a former nerd and popular jock respectively) have been out of school for seven years, which is an eon in high school time. In that span, not only have they aged–the values, the currency and the cultural markers of high school have all changed. In an inversion of the usual kids-are-going-to-hell narrative, they find that suddenly nerds are respected, diversity is encouraged, tough guys are sneered at and caring–about grades or your car’s environmental footprint–is cool. They graduated in 2005, but that might as well be 1965. Jenko, whose good looks now get him nowhere socially, decides: “It’s Glee’s fault. Fuck Glee!” (Ironically, there’s something slightly Finn Hudsonish about Jenko, who evolves from jock to sensitive honorary nerd.)

There’s plenty of more standard cop-and-high-school comedy, but that small fresh idea carries the movie a long way. And it lets the movie address a silliness of the original show that even its fans remember fondly–how old the undercover characters looked, like many stars of high school shows–without doing it as simple parody. The logarithmic rate of high school change shows up in the littlest things, like when Schmidt calls sorta-love-interest Molly (Brie Larson), and she tells him that she usually just texts; she only talks on the phone when “an elderly relative” calls.

Jump Street, in other words, works because it’s less a remake than a borrowing; it cheerfully admits that the title and the premise are there to get you in the door, then goes on to make a funny comedy, one that, in its tiny way, says a little something about what life is like in 2012. I’ll be interested to see if there’s a similar theme in the upcoming American Pie follow-up, American Reunion–after all, 1999 was another millennium, and now feels like it.

And if there’s a franchise I have even lower expectations for, it’s American Pie. Too bad it’s too late to get Jonah Hill involved in that one.